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Mirrors > Home > ILE Home > Th. List > nfs1v | GIF version |
Description: 𝑥 is not free in [𝑦 / 𝑥]𝜑 when 𝑥 and 𝑦 are distinct. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfs1v | ⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbs1 1938 | . 2 ⊢ ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑) | |
2 | 1 | nfi 1462 | 1 ⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑 |
Colors of variables: wff set class |
Syntax hints: Ⅎwnf 1460 [wsb 1762 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1447 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-11 1506 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 |
This theorem is referenced by: nfsbxy 1942 nfsbxyt 1943 sbco3v 1969 sbcomxyyz 1972 sbnf2 1981 mo2n 2054 mo23 2067 mor 2068 clelab 2303 cbvralf 2696 cbvrexf 2697 cbvralsv 2719 cbvrexsv 2720 cbvrab 2735 sbhypf 2786 mob2 2917 reu2 2925 sbcralt 3039 sbcrext 3040 sbcralg 3041 sbcreug 3043 sbcel12g 3072 sbceqg 3073 cbvreucsf 3121 cbvrabcsf 3122 disjiun 3998 cbvopab1 4076 cbvopab1s 4078 csbopabg 4081 cbvmptf 4097 cbvmpt 4098 opelopabsb 4260 frind 4352 tfis 4582 findes 4602 opeliunxp 4681 ralxpf 4773 rexxpf 4774 cbviota 5183 csbiotag 5209 isarep1 5302 cbvriota 5840 csbriotag 5842 abrexex2g 6120 abrexex2 6124 dfoprab4f 6193 finexdc 6901 ssfirab 6932 uzind4s 9589 zsupcllemstep 11945 bezoutlemmain 11998 nnwosdc 12039 cbvrald 14476 bj-bdfindes 14637 bj-findes 14669 |
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